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QJEEM23Ph41da: JEE Main 2023 Physics - Class 12 JEEM23Ph41da Solution: A ray of light is incident from air on a glass plate having…

A ray of light is incident from air on a glass plate having thickness 3\sqrt3 cm and refractive index 2\sqrt2 . The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ ×\times 10 −2^{-2} cm. (given sin⁡15∘=0.26\sin 15^\circ = 0.26 )

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JEE Main 2023 (Online) 25th January Morning Shift Physics - Geometrical Optics Question 66 English Explanation

sin⁡i=12=45∘\sin i=\frac{1}{\sqrt{2}}=45^{\circ}

⇒\Rightarrow at point (1)

μsin⁡r=sin⁡i=12\mu \sin r=\sin i=\frac{1}{\sqrt{2}}

sin⁡r=12⇒r=30∘\sin r=\frac{1}{2} \quad \Rightarrow \quad r=30^{\circ}

Lateral displacement

=tcos⁡rsin⁡(15∘)=3(32)×0.26=\frac{t}{\cos r} \sin \left(15^{\circ}\right)=\frac{\sqrt{3}}{\left(\frac{\sqrt{3}}{2}\right)} \times 0.26

=2×0.26=2 \times 0.26

=0.52 cm=0.52 \mathrm{~cm} =52×10−2 cm=52 \times 10^{-2} \mathrm{~cm}

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